 | Robert Potts - 1868 - 434 pages
...on the other part, Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. FQ Upon AB describe the square A CDB ; (I. 46.) bisect AC... | |
 | James Maurice Wilson - 1869 - 260 pages
...therefore remembering that AD = DC, we obtain by addition that AB* + BC* = 2AD* + 2DB*. Ex. 3. To divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts is equal to the square of the other part. Let AB be the given line. Construction. Draw a square ACDB... | |
 | Euclides - 1871 - 136 pages
...that BGD is a straight line. /i as a If. a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...whole line BC and each of its parts. PBOPOSITION III. If a right line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangle contained by the two parts. The propositions... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...straight line. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square on the otJter part, is equal to the square on the straight line which is made... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...square on CD. QED PROP. XI.— PKOBLEM. (Euc. II. 11). To divide a straight line into two parts, so that the rectangle contained by the whole line, and one of the parts, may be equal to the square of the other part. Let AB be a straight line, it is required to find a point... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...rectangle BP, PQ + rectangle BP, QC. Hence, if a straight line be divided into any number of parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangles contained by that part and the other... | |
 | Edward Atkins - 1874 - 426 pages
...line, &c. QED Proposition 8. — Theorem. If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made... | |
 | Euclides - 1874 - 342 pages
...line, &c. QED PROPOSITION 8. —Theorem. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square on the other part, is equal to the square on the straight line, which is made... | |
 | Euclides - 1874 - 120 pages
...represented in symbols, PROPOSITION 8. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained- by the whole line and one of the parts together with the square on the other part, is equal to the square on the straight line which is made... | |
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Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... 
